Norms on Possibilities. I : Forcing with Trees and Creatures.
- 1st ed.
- 1 online resource (186 pages)
- Memoirs of the American Mathematical Society ; v.141 .
- Memoirs of the American Mathematical Society .
Intro -- Contents -- Annotated Content -- Abstract -- Chapter 0. Introduction -- 0.1. The content of the paper -- 0.2. Notation -- Chapter 1. Basic definitions -- 1.0. Prologue -- 1.1. Weak creatures and related forcing notions -- 1.2. Creatures -- 1.3. Tree creatures and tree-like forcing notions -- 1.4. Non proper examples -- Chapter 2. Properness and the reading of names -- 2.1. Forcing notions Q*[sub(s∞)](K,Σ), Q*[sub(w∞)](K,Σ) -- 2.2. Forcing notion Q*[sub(f)](K,Σ): bigness and halving -- 2.3. Tree-creating (K,Σ) -- 2.4. Examples -- Chapter 3. More properties -- 3.1. Old reals are dominating -- 3.2. Preserving non-meager sets -- 3.3. Preserving non-null sets -- 3.4. (No) Sacks Property -- 3.5. Examples -- Chapter 4. Omittory with Halving -- 4.1. What omittory may easily do -- 4.2. More operations on weak creatures -- 4.3. Old reals are unbounded -- 4.4. Examples -- Chapter 5. Around not adding Cohen reals -- 5.1. (f,g)-bounding -- 5.2. (t,F)-bounding -- 5.3. Quasi-generic Γ and preserving them -- 5.4. Examples -- Chapter 6. Playing with ultrafilters -- 6.1. Generating an ultrafilter -- 6.2. Between Ramsey and p-points -- 6.3. Preserving ultrafilters -- 6.4. Examples -- Chapter 7. Friends and relatives of PP -- 7.1. Balcerzak-Plewik number -- 7.2. An iterable friend of the strong PP-property -- 7.3. Bounded relatives of PP -- 7.4. Weakly non-reducible p-filters in iterations -- 7.5. Examples -- List of definitions -- Bibliography.